As a variant of the Area Under the ROC Curve (AUC), the partial AUC (PAUC) focuses on a specific range of false positive rate (FPR) and/or true positive rate (TPR) in the ROC curve. It is a pivotal evaluation metric in real-world scenarios with both class imbalance and decision constraints. However, selecting instances within these constrained intervals during its calculation is NP-hard, and thus typically requires approximation techniques for practical resolution. Despite the progress made in PAUC optimization over the last few years, most existing methods still suffer from uncontrollable approximation errors or a limited scalability when optimizing the approximate PAUC objectives. In this paper, we close the approximation gap of PAUC optimization by presenting two simple instance-wise minimax reformulations: one with an asymptotically vanishing gap, the other with the unbiasedness at the cost of more variables. Our key idea is to first establish an equivalent instance-wise problem to lower the time complexity, simplify the complicated sample selection procedure by threshold learning, and then apply different smoothing techniques. Equipped with an efficient solver, the resulting algorithms enjoy a linear per-iteration computational complexity w.r.t. the sample size and a convergence rate of $O(\epsilon ^{-1/3})$O(ε-1/3) for typical one-way and two-way PAUCs. Moreover, we provide a tight generalization bound of our minimax reformulations. The result explicitly demonstrates the impact of the TPR/FPR constraints $\alpha$α/$\beta$β on the generalization and exhibits a sharp order of $\tilde{O}(\alpha ^{-1}n_+^{-1} + \beta ^{-1}n_-^{-1})$O˜(α-1n+-1+β-1n--1). Finally, extensive experiments on several benchmark datasets validate the strength of our proposed methods.

The Area Under the Receiver Operating Characteristics Curve (AUC) is a widely used metric for evaluating model performance across all possible decision thresholds. Existing methods for AUC optimization typically assume a predefined parametric distribution of thresholds. However, the optimal decision threshold depends on the misclassification costs, which follow a non-parametric distribution.This motivates us to introduce a variant of AUC, termed Cost-aware AUC (CAUC), where the thresholds are conditioned on an empirically determined cost distribution. Unfortunately, as a bilevel problem, it is challenging to directly optimize the CAUC: 1) The inner problem of finding the optimal thresholds is non-convex, leading to potential issues with convergence; 2) The outer problem involves the derivative of False Positive Rate (FPR) w.r.t. the threshold, which is unavailable without an explicit formulation of threshold distribution. To address challenge 1), we utilize the convex relaxation technique to reshape the inner problem into a convex one. Facing challenge 2), we propose an adaptive kernel density estimation framework. Specifically, the derivative of FPR is considered an aggregation of various kernel functions. To avoid manually crafting the aggregation function, we propose a finite-difference-based stochastic algorithm to optimize the model without explicit aggregation function. Theoretically, the proposed algorithm enjoys a convergence rate of $\mathcal {O}(\epsilon ^{-4})$O(ε-4). Empirical studies across various datasets and cost distributions speak to the effectiveness and soundness of our framework.

Diffusion models have achieved remarkable success across various domains. However, their slow generation speed remains a critical challenge. Existing acceleration methods, while aiming to reduce steps, often compromise sample quality, controllability, or introduce training complexities. Therefore, we propose RayFlow, a novel diffusion framework that addresses these limitations. Unlike previous methods, RayFlow guides each sample along a unique path towards an instance-specific target distribution. This method minimizes sampling steps while preserving generation diversity and stability. Furthermore, we introduce Time Sampler, an importance sampling technique to enhance training efficiency by focusing on crucial timesteps. Extensive experiments demonstrate RayFlow’s superiority in generating high-quality images with improved speed, control, and training efficiency compared to existing acceleration techniques.

Diffusion models have emerged as state‑of‑the‑art in image synthesis.However, it often suffer from semantic instability and slow iterative denoising. We introduce Latent Alignment Framework (LABridge), a novel Text–Image Latent Alignment Framework via an Ornstein–Uhlenbeck (OU) Process, which explicitly preserves and aligns textual and visual semantics in an aligned latent space. LABridge employs a Text-Image Alignment Encoder (TIAE) to encode text prompts into structured priors that are directly aligned with image latents. Instead of a homogeneous Gaussian, Mean-Conditioned OU process smoothly interpolates between these text‑conditioned priors and image latents, improving stability and reducing the number of denoising steps. Extensive experiments on standard text-to-image benchmarks show that LABridge achieves better text–image alignment metric and competitive FID scores compared to leading diffusion baselines. By unifying text and image representations through principled latent alignment, LABridge paves the way for more efficient, semantically consistent, and high‑fidelity text to image generation.

**Diffusion models** achieve remarkable generative performance but are hampered by slow, iterative inference. Model distillation seeks to train a fast student generator. **Variational Score Distillation (VSD)** offers a principled KL-divergence minimization framework for this task. This method cleverly avoids computing the teacher model's Jacobian, but its student gradient relies on the score of the student's own noisy marginal distribution, $\nabla\_{\mathbf{x}\_t} \log p\_{\phi,t}(\mathbf{x}\_t)$. VSD thus requires approximations, such as training an auxiliary network to estimate this score. These approximations can introduce biases, cause training instability, or lead to an incomplete match of the target distribution, potentially focusing on conditional means rather than broader distributional features. We introduce **VarFlow**, a method based on a **Score-Rule Variational Distillation (SRVD)** framework. VarFlow trains a one-step generator $g_{\phi}(\mathbf{z})$ by directly minimizing an energy distance (derived from the strictly proper energy score) between the student's induced noisy data distribution $p_{\phi,t}(\mathbf{x}_t)$ and the teacher's target noisy distribution $q_t(\mathbf{x}_t)$. This objective is estimated entirely using samples from these two distributions. Crucially, VarFlow bypasses the need to compute or approximate the intractable student score. By directly matching the full noisy marginal distributions, VarFlow aims for a more comprehensive and robust alignment between student and teacher, offering an efficient and theoretically grounded path to high-fidelity one-step generation.

Area Under the ROC Curve (AUC) is a widely used ranking metric in imbalanced learning due to its insensitivity to label distributions. As a well-known multiclass extension of AUC, Multiclass AUC (MAUC, a.k.a. M-metric) measures the average AUC of multiple binary classifiers. In this paper, we argue that simply optimizing MAUC is far from enough for imbalanced multi-classification. More precisely, MAUC only focuses on learning scoring functions via ranking optimization, while leaving the decision process unconsidered. Therefore, scoring functions being able to make good decisions might suffer from low performance in terms of MAUC. To overcome this issue, we turn to explore AUCµ, another multiclass variant of AUC, which further takes the decision process into consideration. Motivated by this fact, we propose a surrogate risk optimization framework to improve model performance from the perspective of AUCµ. Practically, we propose a two-stage training framework for multi-classification, where at the first stage a scoring function is learned maximizing AUCµ, and at the second stage we seek for a decision function to improve the F1-metric via our proposed soft F1. Theoretically, we first provide sufficient conditions that optimizing the surrogate losses could lead to the Bayes optimal scoring function. Afterward, we show that the proposed surrogate risk enjoys a generalization bound in order of O(1/√N). Experimental results on four benchmark datasets demonstrate the effectiveness of our proposed method in both AUCµ and F1-metric.

In this paper, we focus on the mural-restoration task, which aims to detect damaged regions in the mural and repaint them automatically. Different from traditional image restoration tasks like in/out/blind-painting and image renovation, the corrupted mural suffers from more complicated degradation. However, existing mural-restoration methods and datasets still focus on simple degradation like masking. Such a significant gap prevents mural-restoration from being applied to real scenarios. To fill this gap, in this work, we propose a systematic framework to simulate the physical process for damaged murals and provide a new benchmark dataset for mural-restoration. Limited by the simplification of the data synthesis process, the previous mural-restoration methods suffer from poor performance in our proposed dataset. To handle this problem, we propose the Attention Diffusion Framework (ADF) for this challenging task. Within the framework, a damage attention map module is proposed to estimate the damage extent. Facing the diversity of defects, we propose a series of loss functions to choose repair strategies adaptively. Finally, experimental results support the effectiveness of the proposed framework in terms of both mural synthesis and restoration.

Long-tailed learning is one of the most challenging problems in visual recognition. There are some studies aiming to solve long-tailed classification from the perspective of feature learning. Recent work proposes to learn the balanced representation by fixing the linear classifier as Equiangular Tight Frame (ETF), since they argue what matters in classification is the structure of the feature, instead of their directions. Holding a different view, in this paper, we show that features with fixed directions may be harmful to the generalization of models, even if it is completely symmetric. To avoid this issue, we propose Representation-Balanced Learning Framework (RBL), which introduces orthogonal matrices to learn directions while maintaining the geometric structure of ETF. Theoretically, our contributions are two-fold: 1). we point out that the feature learning of RBL is insensitive toward training set label distribution, it always learns a balanced representation space. 2). we provide a generalization analysis of proposed RBL through training stability. To analyze the stability of the parameter with orthogonal constraint, we propose a novel training stability analysis paradigm, Two-Parameter Model Stability. Practically, our method is extremely simple in implementation but shows great superiority on several benchmark datasets.

In this paper, we aim to tackle flexible cost requirements for long-tail datasets, where we need to construct a (a) cost-sensitive and (b) class-distribution robust learning framework. The misclassification cost and the area under the ROC curve (AUC) are popular metrics for (a) and (b), respectively. However, limited by their formulations, models trained with AUC cannot be applied to cost-sensitive decision problems, and models trained with fixed costs are sensitive to the class distribution shift. To address this issue, we present a new setting where costs are treated like a dataset to deal with arbitrarily unknown cost distributions. Moreover, we propose a novel weighted version of AUC where the cost distribution can be integrated into its calculation through decision thresholds. To formulate this setting, we propose a novel bilevel paradigm to bridge weighted AUC (WAUC) and cost. The inner-level problem approximates the optimal threshold from sampling costs, and the outer-level problem minimizes the WAUC loss over the optimal threshold distribution. To optimize this bilevel paradigm, we employ a stochastic optimization algorithm (SACCL) to optimize it. Finally, experiment results show that our algorithm performs better than existing cost-sensitive learning methods and two-stage AUC decisions approach.

The Partial Area Under the ROC Curve (PAUC), typically including One-way Partial AUC (OPAUC) and Two-way Partial AUC (TPAUC), measures the average performance of a binary classifier within a specific false positive rate and/or true positive rate interval, which is a widely adopted measure when decision constraints must be considered. Consequently, PAUC optimization has naturally attracted increasing attention in the machine learning community within the last few years. Nonetheless, most of the existing methods could only optimize PAUC approximately, leading to inevitable biases that are not controllable. Fortunately, a recent work presents an unbiased formulation of the PAUC optimization problem via distributional robust optimization. However, it is based on the pair-wise formulation of AUC, which suffers from the limited scalability w.r.t. sample size and a slow convergence rate, especially for TPAUC. To address this issue, we present a simpler reformulation of the problem in an asymptotically unbiased and instance-wise manner. For both OPAUC and TPAUC, we come to a nonconvex strongly concave min-max regularized problem of instance-wise functions. On top of this, we employ an efficient solver that enjoys a linear per-iteration computational complexity w.r.t. the sample size and a time-complexity of $O(\epsilon^{-1/3})$ to reach a $\epsilon$ stationary point. Furthermore, we find that the min-max reformulation also facilitates the theoretical analysis of generalization error as a byproduct. Compared with the existing results, we present new error bounds that are much easier to prove and could deal with hypotheses with real-valued outputs. Finally, extensive experiments on several benchmark datasets demonstrate the effectiveness of our method.